Definition: Present value

Category: External debt - IMF

The present value is the discounted sum of all future debt service at a given rate of interest. If the rate of  interest is the contractual rate of the debt, by construction, the present value equals the nominal value, whereas if the rate of interest is the market interest rate, then the present value equals the market value of the debt. 

In debt-reorganization discussions, the present value concept is used to measure, in a consistent manner, the burden sharing of debt reduction among creditors. This can be illustrated by the following example. 

Debtor A owes 100 to both creditor B and creditor C. The maturity of both loans is the same. Creditor B’s loan has an interest rate of 3 percent and that of C an interest rate of 6 percent. The "market rate" is assumed to be 8 percent—that is, B and C could have lent the money at this higher rate. So, for both B and C, the opportunity cost of lending at their respective interest rates, rather than at the market rate, can be calculated by discounting future payments at the market rate of 8 percent (present value), and comparing the outcome with the outstanding nominal value of 100. If PV(B) represents the present value for B and PV(C) represents the present value for C, then: 

PV(B) < PV(C) < 100 

PV(B) is less than PV(C) because the size of the future payments to be made by A to B is less than those to be made to C. In turn, the payments by A to C are less than would have been the case if a market rate of interest had been charged. This is illustrated by the annual interest payments. Debtor A would annually pay 3 to B; 6 to C; and 8 at the market rate of interest. 

In deciding upon burden sharing of debt reduction, since B’s claims on A are already lower than those of C, despite the same nominal value, debt reduction required from B might well be less than that required from C. So, it can be seen that by using a common interest rate to discount future payments, the burden on the debtor of each loan can be quantified in a comparable manner. http://ec.europa.eu/eurostat/ramon/statmanuals/files/external_debt_guide_2003_EN.pdf#page=255